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There are deep connections between the theory of algorithms and dynamical systems theory.

On one hand, the transformations of data effected by an algorithm can be considered as a dynamical system and the techniques of dynamical systems can be used to analyze properties such as global convergence, asymptotic rates, etc., and eventually lead to better numerical algorithms.

On the other hand, computations in dynamical systems present special challenges. For example, the objects to be discretized are geometric objects or have a very strong algebraic component. What is known a priori of the solutions affects the design of algorithms. Suitably designed algorithms may be used as ingredients in rigorous proofs.